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International Journal of Mathematics and Mathematical Sciences
Volume 8, Issue 4, Pages 707-717

A representation of Jacobi functions

1Department of Applied Mathematical Sciences, University of Houston-Downtown, Houston 77002, Texas, USA
2Department of Mathematics & Statistics, University of Regina, Regina S45 0A2, Canada

Received 1 August 1985

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recently, the continuous Jacobi transform and its inverse are defined and studied in [1] and [2]. In the present work, the transform is used to derive a series representation for the Jacobi functions Pλ(α,β)(x), ½α, β½, α+β=0, and λ½. The case α=β=0 yields a representation for the Legendre functions and has been dealt with in [3]. When λ is a positive integer n, the representation reduces to a single term, viz., the Jacobi polynomial of degree n.